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Input-to-state Stability of Nonlinear Positive Systems

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Abstract

In this paper, input-to-state stability (ISS), as a useful tool for robust analysis, is first applied to continuous-time and discrete-time nonlinear positive systems. For continuous-time and discrete-time positive systems, some new definitions of ISS are introduced. Different from the usual ISS definitions for nonlinear systems, our ISS definitions can fully reflect the positiveness requirements of states and inputs of the positive systems. By introducing the max-separable ISS Lyapunov functions, some ISS criterions are given for general nonlinear positive systems. Based on that, the ISS criterions for linear positive systems and affine nonlinear homogeneous systems are given. Through them, the ISS properties can be judged directly from the differential and algebraic characteristics of the systems. Simulation examples verify the validity of our results.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, P. R. China

    Yan Zhao & Fanwei Meng

  2. School of Mathematical Sciences, University of Jinan, Jinan, 250022, P. R. China

    Yan Zhao

Authors
  1. Yan Zhao
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  2. Fanwei Meng
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Correspondence to Fanwei Meng.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Juhoon Back under the direction of Editor Jessie (Ju H.) Park. This work was supported by the National Natural Science Foundation of China (Grant No. 11671227, 61374074), Science and technology project of University of Jinan (Grant No. XKY1701).

Yan Zhao received her B.S. degree from the University of Jinan, China, in 2002 and her M.S. degree from the Qufu Normal University, China, in 2005. She is currently a doctoral student of the Qufu Normal University and a teacher of the University of Jinan. Her research interests are in the stability theory and nonlinear systems.

Fanwei Meng received his B.S. and M.S. degrees from the School of Mathematical Sciences, Qufu Normal University, China, in 1983 and 1988, respectively. He received his Ph.D. degree from China Academy of Engineering Physics in 2003. He is a professor with the School of Math-ematical Science, Qufu Normal University since 1995, and the director of School of Mathematical Science, Qufu Normal University since 2009. His research interests include stability theory and qualitative theory of order differential equation, Hamiltonian systems and Fractional order differential equation.

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Zhao, Y., Meng, F. Input-to-state Stability of Nonlinear Positive Systems. Int. J. Control Autom. Syst. 17, 3058–3068 (2019). https://doi.org/10.1007/s12555-018-0715-4

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  • DOI: https://doi.org/10.1007/s12555-018-0715-4

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